stirling
DESCRIPTION
stirling engineTRANSCRIPT
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AbstractThe principle of a new design of Free Piston
Stirling Engine (FPSE) prototype for small-scale power
generator, such as solar dish Stirling engine, has been described
in this paper. The design uses a special bellows with high
reliability and long life mechanical springs displacer and power
piston. A mathematical model has been developed to analyze the
thermal and dynamic performance of the engine as well as to
evaluate the output power and thermal efficiency of the cycle.
Two methods of Stirling cycle analysis, which are Ideal
Adiabatic and Simple Analysis, were carried out in order to
calculate the performance and efficiency of the conserved FPSE
design. A computer program is in progress so that the thermal
cycle of Stirling simulated. The results extracted from the
simulation proved a valuable thermal efficiency and overall
satisfactory performance for the new FPSE design.
Index TermsStirling engine, free piston, power generation,
low temperature, small-scale system.
I. INTRODUCTION
Stirling engines are external combustion machines that can
operate on any kind of thermal energy including waste heat,
solar and biofuel heat sources. Stirling heat engine has long
been proposed as a simple, reliable and efficient prime mover
that converts heat to mechanical power for power generation.
Despite huge research and development efforts on kinematic
Stirling machine, it has proved difficult to compete against
internal combustion counterpart due to problems of working
fluid seals, lubrication and leakage [1]. Recently there has
been interest in developing the Free Piston Stirling Engine
(FPSE) configuration to address the design and reliability
limitations of the kinematic type. Numerous advances in
FPSE design have been demonstrated since its invention by
Beale in the early 1960s. Similarly, a mathematical formulation of the Stirling cycle was only published 50 years
later after its invention by the Robert Stirling in 1816. This
analysis was made by Gustave Schmidt in 1871 [2]. The
attractiveness of this analysis is that it produces closed-form
solutions for the performance of the Stirling cycle [3]. Today,
the design and performance analysis of a Stirling engine is
carried out using the empirical and analytical models. The
empirical models are mostly based on a dimensionless
parameter called Beale number to predict the engine power
depending on the engine other operating parameters such as
frequency, pressure and swept volume and the analytical
models are based on dynamic and thermodynamic analysis.
Generally, the thermodynamic analysis of a Stirling engine
Manuscript received May 4, 2014; revised June 22, 2014.
S. Ghozzi and R. Boukhanouf are with The University of Nottingham,
Department of Built Environment, Nottingham, UK (e-mail:
[email protected], [email protected]).
cycle is very complex. This work presents the second-order
analysis [4] which is more complex than Schmidt analysis as it
eliminates the assumption of isothermal working spaces and
ideal heat exchangers. The analysis also takes into account
heat and pumping losses and regenerator inefficiencies. The
computer codes have been developed and adopted for a novel
Free Piston Stirling engine configuration to determine its
design main parameters and predict the thermal performance
in terms of its output power and thermal efficiency.
II. DESCRIPTION OF THE FPSE TOPOLOGY
The Free Piston Stirling Engine (FPSE) is made of two
working space volumes, the expansion and compression
space, which form part of the heat source and heat sink
respectively. As shown in the proposed design of Fig. 1, these
spaces are coupled through the heater, regenerator and cooler.
The heater is a simple flat stainless steel plate. Sensible heat
energy released in the combustion chamber is transferred
though the heater wall to the working fluid in the engine. The
cooler is made of an annular water jacket surrounding the
compression space [5]. The regenerator is made of fine wire
meshes and is packed in an annulus gap around the engine
cylinder. The purpose of the regenerator is to store heat
energy of the working fluid as it cycles between the expansion
and compression space. If properly design, the regenerator
will allow an increase of the efficiency of the Stirling cycle as
it reduces large temperature swings in the expansion and
compression space. The heat energy supply to the engine is
does work on the working fluid which expansion and
compression drives a power piston. A second piston
(displacer) is located between the expansion space and the
compression space circulates the working fluid between the
expansion and compression space [6].
Fig. 1. General scheme for free piston stirling engine.
A. The Proposed Design of FPSE
Initially, a number of designs for the FP engine with
bellows that can be practically manufactured have been
proposed. However, the assembly and manufacture issues
Computer Modeling of a Novel Mechanical Arrangement
of a Free-Piston Stirling Engine
S. Ghozzi and R. Boukhanouf
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Journal of Clean Energy Technologies, Vol. 3, No. 2, March 2015
DOI: 10.7763/JOCET.2015.V3.184
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were taking into considerations in order to simplify the
assembly and reduce the total cost. The displacer is made of
light weight sealed metal cylinder. Since the displacer is
located between the expansion space and the compression
space, it experiences a large temperature gradient. The
displacer is supported by a specially shaped metal bellows
that act as mechanical springs. The bellows were designed to
achieve a specific operating frequency and displacer stroke.
Similarly, the power piston is mounted on another metal
bellows to form a mass-spring oscillating component so that it
is in position of free moving. The mechanical arrangement of
the components of the engine is shown in Fig. 2. The sealed
working fluid of the engine are cooled and heated through.
For simplicity, the regenerator used in this engine is of the
annular regenerator type that is housed around the displacer.
B. Bellows Spring Design
One of the main critical components of this design is the
metal bellows that act as supporting mechanical springs for
both the displacer and the power piston. The bellows were
designed to have specific characteristics to meet the engine
operating parameters. This includes, the bellows spring rate,
maximum allowable stroke, operating temperature and
number of operating cycles before failure. Fig. 3 shows a
schematic diagram of the bellows used in the engine.
Fig. 2. The proposed design of the FPSE.
Fig. 3. General scheme for the bellows used in the engine.
III. OUTLINE OF THERMAL MODELLING
The thermal modelling of the engine was conducted using
second order mathematical analysis based on finite cell
method. This consists in subdividing the working fluid
flow-passages, that is heat exchangers and connecting ports,
into five homogenous control volumes; namely expansion
space, heater, regenerator, cooler and compression space.
Throughout this analysis it was assumed that perfect gas laws
apply in each control volume and the flow is one-dimensional.
Fig. 4 shows heat balance of a typical control volume cell.
The expansion and compression control volumes were
assumed to be sinusoids and adiabatic. The temperature of the
heater and cooler were assumed to be constant and known and
defined as initial conditions. The temperature gradient in the
five control volumes of the engine is presented in Fig. 5.
The adiabatic model formulation was derived by applying
the perfect gas laws, conservation of energy, mass, and
momentum to each control volume as follows [7]:
RTdmdWdQ (1)
mRTPV (2)
oi mmdm (3)
The differential form of the equation of state is given as
following:
T
dT
m
dm
V
dV
P
dP (4)
The values of heat transfer (Q) for the heater and cooler
cells are then used determine the actual operating temperature
of the working fluid in the heater and cooler, as following:
wgkkkwkk AhQTT / (5)
wghhhwhh AhQTT / (6)
In this analysis, irreversibilites due to heat, pressure and
friction losses in the heat are considered through using the
number of transfer units (NTU) method. The heat exchangers
effectiveness is then defined as follows [8]:
NTUNTU
1 (7)
where the NTU is expressed as:
2AANNTU wST (8)
And Stanton Number is given by:
pST uchN (9)
The working fluid pumping losses expressed as pressure
drop across the heat exchangers is evaluated with reference to
the compression space pressure as:
hd
LufP
2
2 (10)
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Therefore, the effective engine work output could be given
as follows:
WWPdVdVdVPW iece (11)
where (Wi) is the work done per cycle that is obtained from
the ideal adiabatic analysis and (W) is the pumping loss per
cycle.
Equation (1), (2), (3) and (4) were set up for every control
volume and then solved simultaneously using a second order
Runge-Kutta method. It was assumed that the movement of
the displacer and power piston are sinusoids and the operating
frequency, working fluid mass, fluid type, and the geometry of
the system were specified. The model was set up so that
according to Urieli [2] it could be solved as an initial-value
problem by assigning an appropriate initial conditions and
integrating the differential equations until a steady state was
reached.
The simulation computes all engine parameters over one
complete thermodynamic cycle including the pressure and
volume variation, cyclic energy input and output of the engine
components, working fluid temperatures variation, and
overall efficiency of the cycle.
Fig. 4. The indicated variables for the Ideal Adiabatic approach [8].
Fig. 5. Temperature variation of Simple analysis model [9].
IV. SIMULATION RESULTS AND DISCUSSION
The design of the engine shown in Fig. 2 was analyzed and
simulated in order to evaluate and validate the performance of
the new engine design and calculate the output power with
taking in consideration the pumping losses caused by the fluid
friction as well as the imperfect of the heat exchangers. The
operating parameters and the engine dimensions used in the
simulation were defined by the user and identified to meet the
criteria and the dimensions of a small scale proof-of-concept
to be tested in the lab, which is under construction. The
operating parameters and conditions are listed in Table I and
the numerical results obtained from the simulation are
presented in Table II. The temperature gradient in the cooler
and heater and the ideal thermal performance of the engine
(heat and frictional losses has yet not considered) are listed in
the top of Table II. However, the actual engine performance
(heat and frictional losses are considered) and the imperfect
specifications of the regeneration.
Fig. 6 shows pressure variation in the expansion and
compression space of the engine and the two pressure
waveforms are nearly in phase, which underpins low pressure
losses in the heat exchangers. On the other hand, the shift of
the pressure variations of the Simple analysis from the
Schmidt pressure variation is due to the perfect regeneration
assumptions in the Schmidt analysis. Furthermore, it is
observed that the maximum pressure is at 140 for both
analyses. Fig. 7 shows gas flow rate (GA) swept by the
displacer and power piston between the engine cells in which
a 90 phase-shift was assumed and quasi-steady-flow is
implied, thus the pressure at any moment is constant
throughout the engine.
TABLE I: OPERATING PARAMETERS FOR THE SIMULATION
Variable Value Unit
Cold side wall temperature (Tk) 50 C
Hot side wall temperature (Th) 300 C
Mean operating pressure (Pmean) 2 bar
Operating frequency (f) 20 Hz
TABLE II: NUMERICAL RESULTS FROM SIMPLE ANALYSIS
Variable name Value Unit
User defined cold side wall temperature (Twk) 50 C
Simulated cold side gas temperature (Tk) 60.4 C
User defined hot side wall temperature (Twh) 300 C
Simulated hot side gas temperature (Th) 277.6 C
Gas mass 0.11 g
Pressure phase angle (beta) 38.2 degree
Schmidt thermal efficiency 44 %
Schmidt total outpour power 0.85 W
Thermal efficiency of thermodynamic cycle 39 %
Total output power of thermodynamic cycle 0.73 W
Heat power added by heater 1.87 W
Heat power rejected by cooler -1.15 W
Regenerator effectiveness 10 %
Regenerator net enthalpy loss 107.9 W
Regenerator wall leakage 11.7 W
Actual total output power 0.73 W
Actual heat power required 121.5 W
Actual efficiency ~1 %
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 3601.9
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2
2.01
2.02
2.03
2.04
2.05
2.06
2.07
2.082.08
Theta in (degrees)
Wo
rkin
g S
pac
e P
ress
ure
in
(b
ars)
Schmidt pressure
mean pressure
comp. space pressure
exp. space pressure
Fig. 6. Pressure variations in working spaces.
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0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360-5
-4
-3
-2
-1
0
1
2
3
4
5x 10
-5
Theta (degrees)
mas
s fl
ow
(K
g/r
ad)
Total mass flow (Kg/rad) GACK GAKR GARH GAHE
Fig. 7. Gas mass flow rate between the working spaces.
Fig. 8 shows a plot of the PV diagram which enclosed area
is a measure of the power output of the engine. Although the
PV diagrams are not in phase, it can be seen that the enclosed
area of the both diagrams are almost similar. As consequence,
the output powers of the both analyses are relatively similar.
Referring to Table II, the output power of Schmidt stands at
(0.85 W) and that of the simple analysis equals to (0.73 W).
Heat transferred between the working spaces and the by the
regenerator is presented in Fig. 9. It is observed that the heat
rejected by the cooler (Qk) and the heat added by the heater
(Qh), both were not that a huge values due to limited
differential temperatures applied beside the small size of the
engine.
670 672 674 676 678 680 682 684 686 688 690 692 694 696 698 7001.95
1.96
1.97
1.98
1.99
2
2.01
2.02
2.03
2.04
2.052.05
Volume (cc)
Pre
ssu
re (
ba
r)
Simple PV Schmidt PV
Fig. 8. PV diagram.
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360-4
-3
-2
-1
0
1
2
3
Theta (dgrees)
Hea
t tr
ansf
erre
d (
J)
QK QH QR
Fig. 9. Cyclic heat transferred within the engine cells.
Fig. 10 shows the temperature variations of the simple
analysis model. It can be noticed that the mean effective
temperature (gas temperature) for the real heater (Th) and
cooler (Tk) are respectively higher and lower than that of the
heat exchanger wall temperatures (Twh) and (Twk). Therefore,
the engine operates on temperature limits lower than that
originally specified; consequently, the performance of the
engine is negatively affected.
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360200
225
250
275
300
325
350
375
400
425
450
475
500
525
550
575
600
625
650
Crank Angle (theta) in (degrees)
Tem
pera
ture
in
(K
)
Tcomp Texp twk tk tr th twh
Fig. 10. Temperature gradient in the engine cells with the crank angle.
V. CONCLUSION AND FURTHER WORK
In conclusion, three simulation methods of varying
complexity, which are the well-known Schmidt analysis, the
Ideal Adiabatic analysis and the so-called Simple analysis,
were implemented to analyze the thermodynamic cycle of a
new design of Free-Piston Stirling engine and to calculate the
output power and thermal efficiency of the engine as well as to
evaluate the performance of the engine. The operating
parameters and the size of the engine were determined to meet
the criteria of a prototype of a small scale proof-of-concept is
under construction to be tested in the lab to prove the results
from the simulation. Referring to slightly low temperature
limits (50-300 C) and low pressure (2 bar) identified by the
user and the low effectiveness of the regenerator (10%) used
in the engine, its output power and thermal efficiency are
satisfactory. Additional complex simulation method (Quasi
Steady-State Flow method) is in progress to evaluate the
methods used in this work and to extract further results in
more details. On the other hand, a small scale
proof-of-concept engine prototype will be tested in the lab to
demonstrate the new design concept.
APPENDIX
Nomenclature:
P: Pressure (Pa)
Pmean: Mean pressure (Pa)
V: Volume (m3)
T: Temperature (K)
W: Power output (W)
Q: Heat energy (J)
m: Mass (kg)
fr: Engine operating frequency (Hz)
f: Friction factor (-)
L: Length (m)
d: Diameter (m)
u: Velocity (m/s)
: Density (kg)
: Angular frequency (rad/s)
GA: Mass flow rate (Kg/rad)
NTU: Number of Thermal Units (-)
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Re: Reynolds Number (-)
NST: Stanton Number (-)
reg: Regenerator effectiveness (%)
h: Heat transfer coefficient (W/m2 K)
Cp : Specific heat capacity at constant pressure (J/kg K)
Cv : Specific heat capacity at constant volume (J/kg K)
ACKNOWLEDGMENT
The authors would like to acknowledge the financial
support from the Libyan government in the form of PhD
scholarship.
REFERENCES
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Great Britain: Adam Hilger Ltd, 1984.
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Salem Ghozzi has obtained his BEng degree in
mechanical engineering, refrigeration & air
conditioning, from Faculty of Industrial Technology,
Misurata, Libya in 2001. He also graduated with MSc
degree in new & renewable energy from the University
of Durham, UK in 2010. Currently, he is a PhD
researcher working on design and development of
Stirling engine technology at the University of
Nottingham, UK. Mr. Ghozzi had worked as a teacher
assistant in the University of Misurata, 2004-2007 and as Field Engineer for
Al-Madar Al-Jadid for Mobile Networks, 2005-2008 and as Power & Air
Con. Manager, 2011-2012.
R. Boukhanouf is a lecturer in sustainable energy
technologies at the Department of Built Environment,
University of Nottingham. His experience in research
and teaching in the area of energy efficient and low
carbon technologies extends for over 15 years. He
obtained his PhD degree in 1996 from the University
of Manchester, UK.
Dr. Boukhanouf worked on numerous research
projects funded by industry and government agencies
in the area of small scale combined heat and power, active and passive
heating and cooling systems for buildings, and advanced heat transfer
enabling devices. He published a number of journal and conference papers
and is named as the inventor in six international patents.
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